The Black Cats fought back after going behind to clinch a 1-1 draw with Swansea at the Stadium of Light to remind the Dutchman of the resilience they showed during his nine-game rescue mission at the end of the last campaign.
Advocaat said: "It's a much better feeling this time, 1-1 against a very good side
Swansea are a good team with good players, but the way we played with the spirit we showed last year, you can see that you will get results.
"With a little bit of luck, if the referee had given us the penalty that was a penalty, we could even have won
But I can live with 1-1, to be fair to Swansea as well
"
Swansea took the lead somewhat against the run of play in first-half injury-time when Kyle Naughton picked out Bafetimbi Gomis' run into the box and he finished effortlessly with a first-time strike.
However, Jermain Defoe was similarly lethal when presented with the chance to level from Jeremain Len's 62nd-minute pass, although it took a series of fine saves by Costel Pantilimon to secure a point.
Sunderland thought they should have been awarded a 66th-minute penalty after Jack Rodwell's shot appeared to come off defender Ashley Williams' arm, but referee Neil Swarbrick was unmoved, much to Advocaat's astonishment.
Asked if it was a penalty, he said: "Yes, 100 per cent - at least the way they are now giving penalties, it was a penalty
I could see it on television and it is clearly against his hand."
The 67-year-old was nevertheless able to reflect upon a positive afternoon and a telling contribution from Defoe, who this week found himself at the centre of rumours that he had asked for a transfer and was being courted by Bournemouth.
He said: "That's the reason he is a striker
He's there to score goals
It was a good goal, a good action
Jermain is a very positive guy.
"Like I told you last week, he never came to me to leave the club or whatever, he never mentioned that
That was not fair to him, but the fans were really behind him today."
Swansea boss Garry Monk left Wearside disappointed at the result after seeing his side create more than enough chances to win the game, but for the excellence of Pantilimon, who produced a superb save to keep out Gomis' 74th-minute header.
Asked for his reaction, Monk said: "Slight disappointment, just because we knew that Sunderland would have a reaction today - it was clear what people were talking about in the week was never going to be the case, that we'd come up here and they'd roll over.
"But we got a good goal and coming in at half-time, that's the position you want to be in
That first 20 minutes of the second half, it was dominance
We were creating chance after chance, and that was what cost us the extra two points
We were so dominant in that period.
"But due to some good goalkeeping from the Sunderland goalkeeper and some probably less clinical finishing from us, we couldn't make it count
We really should have put the game to bed in that period and got that second goal, and possibly another."
Source : PA
Source: PA